Some solvable automaton groups
By Laurent Bartholdi, Zoran vSuni'k. 2006
58 citations recorded by the source corpus.
It is shown that certain ascending HNN extensions of free abelian groups of finite rank, as well as various lamplighter groups, can be realized as automaton groups, i.e., can be given a self-similar structure. This includes the solvable Baumslag-Solitar groups BS(1,m), for m not +/-1. In addition, it is shown that, for any relatively prime integers m,n>=2, the pair of Baumslag-Solitar groups BS(1,m) and BS(1,n) can be realized by a pair of dual automata. The examples are then used to illustrate more general connections between Schreier graphs, composition of automata and dual automata.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/3bfa76767e5b714187545c1ff43607ff4c5b8c1d
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In Computational Theory and Mathematics
- Zoran Šunikacute
- Rostislav I. Grigorchuk
- Volodymyr V. Nekrashevych
- Miklós Abért
- Zoran Sunic
- B'alint Vir'ag
In Geometry and Topology
- Rostislav I. Grigorchuk
- Zoran Šunikacute
- Volodymyr V. Nekrashevych
- Zoran Sunic
- Miklós Abért
- B'alint Vir'ag
- Ievgen V. Bondarenko
- Laurent Bartholdi
In Molecular Biology
Citations in the corpus
- Asymptotic aspects of Schreier graphs and Hanoi Towers groups (2006, background): “It can be shown that examples of polynomial (even linear) diameter growth are given by the realizations of the lamplighter group in [13] and by Baumslag-Solitar solvable groups BS ( 1 ,n) , n (cid:11)= ± 1, in [4].”